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Income Taxes - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Sep. 30, 2016
Sep. 30, 2026
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2015
Income Taxes [Line Items]                  
Blended statutory tax rate   24.53% 35.00% 35.00%          
Deferred tax asset, provisional income tax amount   $ 104.4              
Transition tax liability for foreign subsidiaries, provisional expense   395.8              
Income taxes payable   389.4              
Deferred tax liabilities related to foreign withholding taxes on future distributions on historic earnings   22.7 $ 0.0            
Deferred tax assets related to U.S. foreign tax credits attributable to the foreign withholding taxes   9.9              
Tax benefit attributable to non-U.S. government sponsored tax incentive programs   $ 52.3 $ 43.4 $ 33.9          
Tax benefit per diluted share attributable to non-U.S. government sponsored tax incentive programs   $ 0.41 $ 0.33 $ 0.26          
Gross unrecognized tax benefits   $ 20.1 $ 31.1 $ 32.4         $ 43.9
Accrued interest and penalties for unrecognized tax benefits   2.5 4.0            
Benefits (expense) recognized for interest and penalties related to unrecognized tax benefits   1.5 $ 1.2 $ (0.1)          
Reasonably possible amount of reduction of gross unrecognized tax benefit in the next twelve months   6.0              
Reasonably possible amount of net reduction to income tax provision in the next twelve months if unrecognized tax benefits were recognized, including the recognition of interest and penalties and offsetting tax assets   5.5              
Scenario, Forecast                  
Income Taxes [Line Items]                  
Blended statutory tax rate 21.00%                
Transition tax liability, percentage due         25.00% 20.00% 15.00% 8.00%  
Other current liabilities                  
Income Taxes [Line Items]                  
Income taxes payable   31.1              
Other liabilities                  
Income Taxes [Line Items]                  
Income taxes payable   358.3              
Non-United States                  
Income Taxes [Line Items]                  
Deferred tax liabilities related to foreign withholding taxes on future distributions on historic earnings   $ 34.8